离散时间信号处理（英文版）chp5-第2讲.pptVIP

5.2 System functions for system characterized by difference equations Difference equation: Example 5.2 Find the difference equation of the given system function 5.2.1 Stability and Causality Example 5.3 Determining the ROC Example 5.5 Find the inverse of the given system 5.2.3 Impulse response for rational system functions Example 5.7 A simple FIR system 5.3 Frequency response for rational system functions Three parameters of frequency response Three parameters of frequency response Three parameters of frequency response Sketch frequency response by Geometric method First-order FIR (a single zero) system First-order IIR (a single pole) system First-order IIR (a single pole) system Example 5.8 Example 5.8 Summary 单位圆附近的零点位置对幅度响应凹谷的位置和深度有明显的影响，零点在单位圆上，则幅度响应为0。 在单位圆内且靠近单位圆附近的极点对幅度响应的凸峰的位置和深度有明显影响；极点在单位圆上，则幅度响应为无穷大；极点在单位圆外，则系统不稳定。 适当控制零点、极点的分布，就能改变数字滤波器的频率响应特性，以达到预期的设计要求。 Homework 5.4, 5.6, 5.8, 5.36 System function: ZT straightforward relationship IZT Solution: same algebraic expression for H(z) different choices for ROC different h[n] Causal: Stable: ROC includes the unit circle (|z|= 1). Causal and stable: All poles are inside the unit circle. different system same difference equation ROC: ROC: h[n]: right-sided h[n]: absolutely summable The difference equation does not uniquely specify a LTI system. ROC ——causal, not stable ——stable, not causal ——neither causal nor stable Solution: 5.2.2 Inverse systems Question: What about the the ROC of Hi(z) ? Answer: The ROCs of Hi(z) and H(z) must overlap. The poles of Hi(z) are the zeros of H(z), and vice versa 5.2.2 Inverse systems 1) Not all systems have an inverse, e.g. Ideal lowpass filter. 2) Multi inverse system may exist for a system, example 5.5 Note: —— both causal and stable —— causal and unstable —— stable and noncausal (assumed to be causal) infinite impulse response (IIR) SY finite impulse response (FIR) SY IZT N ≠ 0: N = 0: zeros: poles: The pole at z=a is canceled by zero at z1=a M